A lifelong Democrat, Dimon supported Barack Obama in 2008 and during the aftermath of the financial crisis.

As post-financial-crisis Dodd-Frank regulation started to make an impact on the American financial system, however, he became much more critical.

On Wednesday, after Trump won Tuesday's presidential election, Dimon sent a memo to JPMorgan employees calling them to come together for the nation. He also made a subtle dig at Trump's stances on immigration and race.

"We have just been through one of the most contentious elections in memory, which can make it even harder to put our differences aside," the memo said. "But that makes it more important than ever to bind the wounds of our nation and to bring together Americans from all walks of life. Recognizing that our diversity is a core strength of our nation, we must all come together as fellow patriots to solve our most serious challenges."

JPMorgan declined comment to Business Insider about Trump's possible interest in Dimon as Treasury secretary. Steven Mnuchin, a former Goldman Sachs official, is also reportedly in the running for the position.

Dimon signaled at a JPMorgan conference last month that he expected Democrat Hillary Clinton to win the election.

"I hope the next president, she reaches across the aisle," he said.

Trump has been critical of Dimon in the past too. In 2013 he raised an eye at the CEO for settling a civil-suits against the bank.

"I don't believe in settling cases," Trump told Bloomberg. "I'm not Jamie Dimon, who pays $13 billion to settle a case and then pays $11 billion to settle a case and who I think is the worst banker in the United States."